Problem: Simplify the following expression: $7\sqrt{117}$.
Solution: First, try to factor a perfect square out of the radical. $= 7\sqrt{117}$ $= 7\sqrt{9 \cdot 13}$ Separate the radical and simplify. $= 7\sqrt{9} \cdot \sqrt{13}$ $= 7 \cdot 3 \cdot \sqrt{13}$ $= 21\sqrt{13}$